Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T04:59:02.699Z Has data issue: false hasContentIssue false
  • English
  • Français

FINITELY GENERATED GRADED MULTIPLICATION MODULES

Published online by Cambridge University Press:  01 August 2011

NASER ZAMANI
NASER ZAMANI*
Affiliation:
Faculty of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R = ⊕i ∈ ℤRi be a ℤ-graded ring and M = ⊕i ∈ ℤMi be a graded R-module. Providing some results on graded multiplication modules, some equivalent conditions for which a finitely generated graded R-module to be graded multiplication will be given. We define generalised graded multiplication module and determine some of its certain graded prime submodules. It will be shown that any graded submodule of a finitely generated generalised graded multiplication R-module M has a kind of primary decomposition. Using this, we give a characterisation of graded primary submodules of M. These lead to a kind of characterisation of finitely generated generalised graded multiplication modules.

Keywords

13A0213C0513C1313C99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 693 - 705
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Abd EL-Baset, Z. and Smith, P. F., Multiplication modules, Comm. Algebra 16 (4) (1988), 755–779.CrossRefGoogle Scholar
2.Ali, M. and Smith, D., Some remarks on multiplication and projective modules, Comm. Algebra 32 (2004), 3897–3909.CrossRefGoogle Scholar
3.Anderson, D. and Al-Shaniafi, Y., Multiplication modules and the ideal θ(M), Comm. Algebra 30 (2002), 3383–3390.CrossRefGoogle Scholar
4.Barnard, A. D., Multiplication modules, J. Algebra 70 (1981), 303–315.CrossRefGoogle Scholar
5.Bruns, W. and Herzog, J., Cohen–Macaulay rings (Cambridge University Press, Cambridge, UK, 1998).CrossRefGoogle Scholar
6.Ebrahimi Atani, SH. and Ebrahimi Atani, R., Graded multiplication modules and the graded ideal θg(M), Turk. J. Math. 33 (2009), 1–9.Google Scholar
7.Erdogdu, V., Multiplication modules which are distributive, J. Pure Appl. Algebra 54 (1988), 209–213.CrossRefGoogle Scholar
8.Escoriza, J. and Torrecillas, B., Multiplication graded rings, Lect. Notes Pure Appl. Math. 208 (2000), 127–137.Google Scholar
9.Escoriza, J. and Torrecillas, B., Multiplication objects in commutative Grothendieck category, Comm. Algebra 26 (1998), 1867–1883.CrossRefGoogle Scholar
10.Goto, S. and Watanabe, K., On graded rings I, J. Math. Soc. Japan 30 (1978), 172–213.CrossRefGoogle Scholar
11.Hungerford, T. W., Algebra (Springer, New York, 1974).Google Scholar
12.Krull, W., Ûber allgemeine Multiplikationringe, Tohoku Math. J. 41 (1935), 320–326.Google Scholar
13.Larsen, M. D. and McCarthy, P. J., Multiplicative theory of ideals (Academic Press, Maryland Heights, MO, 1971).Google Scholar
14.McCasland, R. L. and Moore, M. E., On radicals of submodules of finitely generated modules, Canad. Math. Bull. 29 (1) (1986), 37–39.CrossRefGoogle Scholar
15.McCasland, R. L. and Moore, M. E., Prime submodules, Comm. Algebra 20 (6) (1992), 1803–1817.CrossRefGoogle Scholar
16.McCasland, R. L. and Smith, P. F., Prime submodules of Noetherian modules, Rocky Mountain J. Math. 23 (3) (1993), 1041–1062.CrossRefGoogle Scholar
17.Matsumura, H., Commutative ring theory (Cambridge University Press, Cambridge, UK, 1986).Google Scholar
18.Nastasescu, C. and Van Oystaeyen, F., Graded ring theory (North-Holland, Amsterdam, Netherlands, 1982).Google Scholar
19.Northcott, D. G., Lessons on rings, modules and multiplicities (Cambridge University Press, Cambridge, UK, 1968).CrossRefGoogle Scholar
20.Smith, P. F., Some remarks on multiplication modules, Arch. Math. 50 (1988), 223–235.CrossRefGoogle Scholar
21.Tuganbaev, A., Distributive and multiplication modules and rings, Math. Notes 75 (2004), 391–400.CrossRefGoogle Scholar